Question 4

If A and B are two mutually exclusive and exhaustive events with $$P(B) = 3P(A)$$, then what is the value of $$P(\overline{B})$$?

Solution

Since P(B) and P(A) are mutually exclusive and exhaustive , thus, P(B)+P(A)=1

But we know that P(B)=3 P(A) , thus substituting in the above equation we get P(B)=3/4 and P(A)=1/4

Now they have asked P(B_) i.e. 1-P(B)=1-(3/4)=1/4

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